1. Field of the Invention
Embodiments of the present invention generally relate to the field of micromechanical variable capacitors, specifically to the act of releasing a digital capacitor in the presence of a residual RF voltage. The inventions described herein can be applied to any micromechanical structure where the difference between latching voltage and actuation voltage needs to be minimized. It allows devices to be made where the spring constant of the cantilever can be engineered to be greater than the electrostatic attraction across the landing contact due to the voltage dropped across the capacitance contact, while the voltage required to turn the device on is unchanged.
2. Description of the Related Art
Micromechanical actuators are based on the simple principal that they will deflect or move in the presence of an external force. The deflection of these actuators typically follows a linear relationship between force and deflection. The slope of this relationship is defined by the materials used, the geometries of the switch and/or legs, and how the switch and/or legs are anchored (Hooke's Law in the general sense).Spring Force=Fspring=K*X  (1)
Where K is the spring constant and X is the displacement.
The external force normally does not follow a linear relationship between its magnitude and the position of the switch. For the case of electrostatics, the force will increase with the square of the position to the control electrode. This situation causes the phenomena of “snap-in” when a critical displacement is reached. The Electrostatic Force FE is given by:
                              F          E                =                                                            ɛ                0                            ⁢              A                                      2              ⁢                                                (                                      Z                    -                    X                                    )                                2                                              ⁢                      V            2                                              (        2        )            
Where A is the area of overlap between the pull down electrode and the micro electromechanical system (MEMS) device, Z is the starting position, ∈o is the permittivity of free space and V is the applied control voltage. Equilibrium is defined when the sum of all forces is zero which yields the classic snap-in behavior for electrostatic MEMS. Once the cantilever jumps to contact the separation between the cantilever and the pull in electrode is greatly reduced and from equation 2 the electrostatic force increases greatly. To allow the cantilever to pull off the control voltage has to be reduced greatly.
FIG. 1A shows the forces acting on the MEMS device vs. the displacement for an electrostatically actuated MEMS device with a linear spring. Note that the vertical scale of the figure has a logarithmic scale, to better show the various points on the graph. The curve labeled Fspring shows the mechanical force vs. the displacement of the spring which varies linearly with displacement. The curves labeled F@V1, F@V2, F@V3 are the electrostatic forces acting on the MEMS device for different applied voltages V1, V2, V3 where V3>V2>V1.
The MEMS displacement at various applied voltages is found by finding the intersection of the mechanical force curve and the electrostatic force curves. For instance when voltage V1 is applied, the MEMS device displaces to point p1. When the applied voltage is increased to V2 the MEMS device displaces to point p2 and when the voltage is increased to V3 the MEMS device displaces to point p3. At this point when the voltage is increased any further there is no longer an intersection of the electrostatic force curve with the mechanical force curve, because the electrostatic force is always larger than the mechanical force. As a result, the device snaps in and displaces to point p4.
When the voltage is subsequently reduced from V3 to V2 the electrostatic force F@V2 at the displaced location p4 is still larger than the mechanical force Fspring so that the device stays displaced at point p4. Once the voltage is reduced to V1 the electrostatic force F@V1 at the displaced location p4 is as large as mechanical force Fspring. Any further reduction of the voltage would result in only one intersection with the mechanical force curve in point p1 and the device will snap back from point p4 to point p1.
FIG. 1B shows the MEMS displacement vs. applied voltage for the MEMS devices with a linear spring. Shown in this figure are the same points as shown in FIG. 1A. During the up-sweep of the applied voltage, the displacement follows the curve labeled pull-in. At an applied voltage of 5V, the MEMS devices displaces to point p1. Then as the voltage is increased to 15V, the device displaces to point p2. When the voltage is increased to 25V, the MEMS device displaces to point p3. Any further increase in voltage would result in the device to snap in to the full displacement and end up in point p4. Then the voltage is reduced and the displacement follows the curve labeled release. When the voltage is reduced to 5V, the displacement stays at 100% of the gap (point p4′). Any further reduction makes the device snap back down to point p1. Thus, the pull-in voltage is 25V and the release voltage is 5V. FIG. 1B shows the large difference between the release voltage (voltage at which the device snaps from position p4′ to position p1) and landing voltage (voltage at which the device snaps from position p3 to position p4).
The large difference between the release voltage and the landing voltage creates a problem for capacitive RF MEMS when it comes to hot switching. Hot switching is defined as the largest RF voltage that can exist between, for example a MEMS cantilever switch and a landing electrode for which the spring constant of the cantilever is able to pull the contact apart when the control voltage is set to zero.
Therefore, there is a need for RF MEMS that are capable of hot switching.